I asked an American friend in Baghdad what Iran is up to there. This is his response:
Iranian activities in Iraq must be viewed in the context of regional considerations and multiple lines of effort.
Clearly Iran has been setting itself up to be a resurgent force and regional power broker for some time, and Iraq is a critical piece of the game board, yet just one piece. Iran stands in opposition to the Gulf States, Saudi Arabia, Israel of course, and the west in general. They stand with the Assad regime in Syria, Nasrallah/Hezbollah in Lebanon, and their global allies in China, Venezuela, and North Korea. The players that they stand neither with nor against, but a little bit of both, include the Turks who they're with on energy and Kurds but against on Syria, the Pakistanis who they stand with in regard to Talibs and Afghanistan and against with Sunni extremists, Shiite Yemenis who oppose Saudis, AQAP, and the Yemeni government, the north African emerging states, to include Egypt, and others.
What we see are not clearly defined operations with named objectives, rather a series of shaping initiatives intended to strengthen allies, develop transportation routes and mechanisms, and undermine the credibility of opposition governments. The end-state is a Persian/Farsi/Shiite Islamic state that is stronger than the other states in a region that is opposed to western powers, presence, and influence. They are shaping a series of lesser engagements that don't rise to the level of justifying western military intervention, but dispose of regimes they are opposed to, beginning with Bahrain and ending with Israel with Lebanon falling to Hezbollah while they were sleeping.
Near term, they cannot allow Syria to fall and are assisting in every possible way. Of concern is that should the Assad regime appear to be near collapse, a diversionary engagement will be directed against Israel by Iranian allies. As a sword can serve more than one purpose, these same antagonists will strike Israel in response to any Israeli or western action taken against Iranian nuclear facilities. While the world watches the right hand engaged in Syria, they miss the left hand working to organize kinetic opposition in Bahrain, Kuwait, and other Gulf States with sizable Shiite populations, which the Saudis, Qataris, and Emiratis will not abide. And then there is Iraq.
While we Americans espouse a "whole-of-government" approach to strategic objectives abroad, the Iranians actually practice it in Iraq. Diplomatically, they have a robust embassy in Baghdad and very active consulates in Erbil, Basrah, and Karbala. They are building upon the P5+1 conference, with the Iraqi Ambassador to Iran stating in August that they were ready to host another round in Baghdad. Iranian Defense Minister Ahmad Vahidi just concluded successful security cooperation talks in Baghdad. Economically, Najaf hotels are mostly owned by Iranian investors who spend more religious tourism money there than they do in Karbala. Iranians export electricity, finished goods, and smuggled oil into Iraq in exchange for hard currency.
On the religious front, there is a full-court PR campaign, to include radio and billboards, to replace Ayatollah Sistani with Ayatollah Shahroudi, an Iranian with a much more aggressive position on clerics and government than the even-tempered Sistani. Through a variety of agencies, Iran continues to fund Husseinyahs and affiliated social service organizations throughout Iraq. They have the remnants of the Badr Corps firmly ensconced in virtually all Iraqi security organizations ensuring that Sunni organizations are targeted, but they are not. Iranian proxies, such as Assaib Ahl Al-Haq (AAH) and Kitaib Hezbollah are being carefully reconciled with Baghdad while retaining arms to threaten those that stand in opposition. They continually dance with the Sadrists in the form of the Promised Day Brigade and lesser affiliates, seeking influence as opposed to outright control. Politicians and prominent civil servants or other civilians generally know better than to speak out against Iran.
Iran is very active, but they are not omnipotent and work within their limitations. They understand that they have just as many foes as they do friends -- thus they are patient. Iran does not seek to dominate the Gulf Region or Middle East today, rather they seek to improve their hand for the coming conflict of tomorrow. By all accounts, they're building a fairly strong hand to play -- perhaps we should consider improving our hand as well.